Makes a colorful mandelbrot set.

colorMandelbrotSet.pde

// you might have to wait a while to see the mandelbrot set. 
// play around with the amount of iterations to get a different result every time!

size(600, 600);// sets the size. 
noLoop();
background(0);// background is black. 
colorMode(HSB, 360, 100, 100);// sets the color mode to HSB values. 
float w = 4;// width of the set 
float h = (w*height)/width;// height of the set

// now take the negative halves of the width and height.
float xmin = (-w/2);
float ymin = (-h/2);

shows the minimum of the xy dimensions (taking place of the real and imaginary dimensions). set to -2 for each.
//float cx = xmin ;
//float cy =  ymin ;
loadPixels();// loads the pixels. 
long maxiter = 100L;// how many iterations it makes. Play around with this! Higher numbers take longer to finish.

//shows the maximum of the xy dimensions (taking place of the real and imaginary dimensions). set to 2 for each
float xmax = xmin + w;
float ymax = ymin + h;

// the change in x and y. 
float dx = (xmax - xmin)/(width);
float dy = (ymax - ymin)/(height);

//equation: z = z^2 + c. This means that for each itration, x = the square of x + the x and the y (the real and the imaginary. 
//this would work for the imaginary because i^2 = -1.)

// does each process along each of the coordinates
float y = ymin;
for(int j = 0; j < height; j++) {
  float x = xmin;
  for (int i = 0; i < width; i++) {
    float a = x;
    float b = y;
    int n = 0;
    while(n < maxiter) {// while it does the process less than the amount of iterations
      float aa =(a * a);//z^2
      float bb =(b*b);//z^2
      float twoab = 2.0 * (a * b);
      a = (aa - bb + x);
      b = (twoab + y);
      if (dist(aa, bb, 0, 0)>4.0){
        break;
      }
      n++;
    }
    if (n == maxiter) {
      pixels[i+j*width] = color(0);
    }else{
      float norm = map(n, 0, maxiter, 0, 1);
      pixels[i+j * width] = color(map(sqrt(norm), 0, 1, n, 255), 100, 100);
    }
    x+= dx;// adds the change in x
  }
  y +=dy;// adds the change in y
}
// eventually makes a grid of pixels
updatePixels();// updates the look for each iteration

// full code on: 
// https://processing.org/examples/mandelbrot.html